Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+6y &= 5 \\ -8x-6y &= -1\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-8x = 6y-1$ Divide both sides by $-8$ to isolate $x$ $x = {-\dfrac{3}{4}y + \dfrac{1}{8}}$ Substitute this expression for $x$ in the first equation. $4({-\dfrac{3}{4}y + \dfrac{1}{8}}) + 6y = 5$ $-3y + \dfrac{1}{2} + 6y = 5$ Simplify by combining terms, then solve for $y$ $3y + \dfrac{1}{2} = 5$ $3y = \dfrac{9}{2}$ $y = \dfrac{3}{2}$ Substitute $\dfrac{3}{2}$ for $y$ in the top equation. $4x+6( \dfrac{3}{2}) = 5$ $4x+9 = 5$ $4x = -4$ $x = -1$ The solution is $\enspace x = -1, \enspace y = \dfrac{3}{2}$.